Cellular vehicle-to-everything (C-V2X) networks provide a promising solution to improve road safety and traffic efficiency. One key challenge in such systems lies in meeting different quality-of-service (QoS) requirements of coexisting vehicular communication links, particularly under imperfect channel state information (CSI) conditions caused by the highly dynamic environment. In this paper, a novel analytical framework for examining the resilience of C-V2X networks in face of imperfect CSI is proposed. In this framework, the adaptation phase of the C-V2X network is studied, in which an adaptation power scheme is employed and the probability distribution function (PDF) of the imperfect CSI is estimated. Then, the resilience of C-V2X networks is studied through two principal dimensions: remediation capability and adaptation performance, both of which are defined, quantified, and analyzed for the first time. Particularly, an upper bound on the estimation's mean square error (MSE) is explicitly derived to capture the C-V2X's remediation capability, and a novel metric named hazard rate (HR) is exploited to evaluate the C-V2X's adaptation performance. Afterwards, the impact of the adaptation power scheme on the C-V2X's resilience is examined, revealing a tradeoff between the C-V2X's remediation capability and adaptation performance. Simulation results validate the framework's superiority in capturing the interplay between adaptation and remediation, as well as the effectiveness of the two proposed metrics in guiding the design of the adaptation power scheme to enhance the system's resilience.